1. Field of the Invention
The invention relates to the field of methods and systems for locating poles and their residues of specimens from impulse responses and related fields of resonance testing.
2. Prior Art
In many fields it is desirable to have a modal analysis of a specimen or object or to know: the resonant frequencies of the specimen or object, or more particularly to know the natural resonant frequencies and their associated damping which is given by the s-plane location of the poles; the state of the system which is given by the complex residues associated with these frequencies. Such information is invaluable for damping large machinery, for structural and flutter analysis and for countless other applications.
For all but the simplest structures, it is generally impractical to obtain a theoretical transfer function or more particularly, a meaningful theoretical location of the poles and their residues. Ideally, the poles and their residues should be determined from empirically derived functions or qualities that are readily measurable or obtainable from the specimen. For example, the location of the poles in the s-plane and their residues should ideally be determinable from some time domain function, such as the impulse or transient response of the specimen.
In the prior art, several methods exist for obtaining the location of the poles in the s-plane and their residues from empirical information, such as impulse response or from a frequency domain representation of the impulse response, such as the Fourier transform of the response. Most, if not all, of these prior art techniques and methods require the use of judgment and provide no straightforward means for determining the required s-plane information. Among the prior art methods and techniques are:
1. Kennedy-Pancu Method, which utilizes curve fitting techniques, Journal of Aeronautical Science, Volume 14, 603-625 (1947).
2. A method disclosed by James C. Davis in an article entitled Modal Modeling Techniques for Vehicle Shake Analysis, Automotive Engineering Congress, Detroit, Michigan, Jan. 10-14 1972, No. 720045.
3. A method for experimental determination of the poles of a structure by multiple shaker excitation disclosed by R. Lewis and D. Wrisley in an article entitled, A System For The Excitation of Pure Natural Modes of Complex Structure, Journal of Aeronautical Sciences, Vol. 17, No. 11, November 1950, Pages 705-723.
4. A general survey article which discusses the problem is An Investigation into the Theory of Resonance Testing, by Bishop and Gladwell, Philosophical Transactions of the Royal Society of London, Volume 255, January 1963, pages 241-280.